Thanks to the developments of new technologies in the past years such as the Feshbach resonance [1]}, the laser cooling [2]}, the optical lattices/boxes [3]}, [4]} and the artificial gauge potentials [5]}, many exciting and fundamental experimental findings in various dimensions are emerging. To name a few,
we mention (1) the realization of spin-orbit interaction in degenerate quantum Fermi gas [6]}, (2) the observation of the quantum-limited spin transport [7]}, [8]} as well as the sound propagation and damping in a 2D Fermi gases [9]} and a 2D Bose gas [10]}, the universal (first-) sound diffusion in a strongly cylindrical optical box [11]}, the second-sound attenuation near the quantum criticality [12]}, [13]}, (3) the observation of a non-Hermitian phase transition in an optical quantum gas [14]}, (4) the observation of superfluidity in a strongly correlated 2D Fermi gas [15]} together with the quantum scale anomaly and the spatial coherence of the system [16]}, the synthetic dissipation and the turbulent flow in low dimensions [17]}, [18]}, [19]}, [20]}, (5) the experimental verification of the generalized hydrodynamics in a strongly interacting 1D Bose gas [21]}, the spin-charge separation in a 1D Fermi gas [22]} and the direct measurements of the compressibility and the EOS of a 2D photon gas inside a box potential [23]}, see Refs. [24]}, [25]}, [26]}, [27]}, [28]}, [29]}, [30]}, [31]}, [32]} for related discussions on these topics.
On the theoretical side, a two-species Fermi gas with mixed
dimensions [33]}, a 3D resonant Bose-Fermi mixture at
zero temperature [34]} as well as the 2D Fermi-Bose dimers with a stable p-wave resonant interaction [35]} were studied.
It was also demonstrated that a multiple-body problem could be effectively mapped to a two-body problem in
a higher dimension [36]}, and the scattering hypervolume for Fermions in 2D was recently investigated [37]}.
In addition, as an important but complicated problem for a strongly-interacting Fermi gas [24]}, [39]}, namely the determination of its EOS at unitary limit (i.e., the system with an infinite large scattering length), Ref. [40]} successfully adopted the \(\epsilon \) -expansion method originated from the theory of second-order phase transition [41]}, [42]}, [43]}, based on the observation that the unitary Fermi gas in 4D is actually an ideal Bose gas, thus the expansion via \(\epsilon =d-4\)  could relatively be easier to develop.
These studies vividly show that explorations of many-body systems in spaces with different dimensions may provide important new insights into certain interesting physical problems. In fact, the dimensionality is not only important for physical problems but also plays very fundamental roles in solving scientific issues for other fields, such as in the massive data subject in computational sciences [44]}, [45]}, [46]}, [47]}, the technique of principal component analysis [48]} is often applied to find the effective low-dimensional manifold (representation) of the high-dimensional data.
